About Hyperproof -- I. Basic Concepts. 1. Comparing Tarski's World and Hyperproof. 2. Proofs of Consequence and Nonconsequence. 3. Sentential Consequence Rules. 4. Proofs of Consistency and Inconsistency -- II. Diagrammatic Reasoning. 5. The Apply Rule. 6. Reasoning by Cases. 7. Independence Proofs -- III. Sentential Reasoning. 8. Sentence Connective Rules. 9. Quantifier and Identity Rules. 10. Axioms and Analytic Consequence. 11. Logic and Observation -- C. The LoFOL Proof System